Implemetation Hints:

you should use a constructor for your Controller that injects the Model

public class App extends Application {

    public static void main(String[] args) {
        launch(args);
    }

    private Pane root;

    @Override
    public void init() {
        Game game = new Game();
        ControllerFactory controllerFactory = new ControllerFactory(game);
        try {
            FXMLLoader fxmlLoader = new FXMLLoader(getFxml());
            fxmlLoader.setControllerFactory(controllerFactory);
            root = fxmlLoader.load();
        } catch (IOException e) {
            LOGGER.debug("error", e);
        }
        RootController rootController = controllerFactory.getRootController();
        game.init();
        rootController.init();
    }

    @Override
    public void start(Stage stage) {
        if (root != null) {
            stage.setScene(new Scene(root));
            stage.setTitle("title");
            stage.show();
        } else {
            LOGGER.debug("error during init");
            Platform.exit();
            System.exit(0);
        }
    }

}

JavaFx Implemetation Hints:

public class App extends Application {

    public static void main(String[] args) {
        launch(args);
    }

    private Pane root;

    @Override
    public void init() {
        Game game = new Game();
        ControllerFactory controllerFactory = new ControllerFactory(game);
        try {
            FXMLLoader fxmlLoader = new FXMLLoader(getFxml());
            fxmlLoader.setControllerFactory(controllerFactory);
            root = fxmlLoader.load();
        } catch (IOException e) {
            //Log output please (I use a Logger for that)
        }
        RootController rootController = controllerFactory.getRootController();
        game.init();
        rootController.init();
    }

    @Override
    public void start(Stage stage) {
        if (root != null) {
            stage.setScene(new Scene(root));
            stage.setTitle("title");
            stage.show();
        } else {
            //Log output please (I use a Logger for that)
            Platform.exit();
            System.exit(0);
        }
    }

}

Game game = new Game();
Controller controller = new Controller (game);

What this points out is that the controller is depending on the Game, but the Game is independent from the Controller.

public class App extends Application {

    public static void main(String[] args) {
        launch(args);
    }

    private Pane root;

    @Override
    public void init() {
        Game game = new Game();
        ControllerFactory controllerFactory = new ControllerFactory(game);
        try {
            FXMLLoader fxmlLoader = new FXMLLoader(getFxml());
            fxmlLoader.setControllerFactory(controllerFactory);
            root = fxmlLoader.load();
        } catch (IOException e) {
            LOGGER.debug("error", e);
        }
        RootController rootController = controllerFactory.getRootController();
        game.init();
        rootController.init();
    }

    @Override
    public void start(Stage stage) {
        if (root != null) {
            stage.setScene(new Scene(root));
            stage.setTitle("title");
            stage.show();
        } else {
            LOGGER.debug("error during init");
            Platform.exit();
            System.exit(0);
        }
    }

}

public class ControllerFactory implements Callback<Class<?>, Object> {

    private final Game game;

    private RootController rootController;

    public ControllerFactory(Game game) {
        this.game = game;
    }

    @Override
    public Object call(Class<?> type) {
        if (type == RootController.class) {
            //inject the Model in the controller
            rootController = new RootController(game); 
            return rootController;
        } else {
            // default behavior for controllerFactory:
            try {
                return type.getDeclaredConstructor().newInstance();
            } catch (Exception exc) {
                exc.printStackTrace();
                throw new RuntimeException(exc); // fatal, just bail...
            }
        }
    }

    public RootController getRootController() {
        return rootController;
    }


}

Conclusion What this points out is that the controller is depending on the Game, but the Game is independent from the Controller.